Vlada Limic
UBC

Lambda-coalescent processes and genealogies

The talk concerns several aspects of a class of stochastic coalescent processes.
These coalescents arise as scaling limits in mathematical population genetics
models. They are ``duals" to measure-valued processes known as (generalized)
Fleming-Viot processes. In special cases the correspondence between the genealogical
process of a (super) diffusion and a coalescent process is well known. The spatial
(or structured) coalescents are particularly important in the study of asymptotic
behavior of a class of interacting particle systems and the corresponding scaling
limits.

I will attempt to describe most of the above relations in the intuitive ``particle
representation" setting. Some interesting properties of (spatial) Lambda-coalescents
will be discussed, as well as very interesting consequences for the asymptotics of
the related interacting particle systems and their scaling limits.